Advantages of Calculating Shear-wave Velocity From Surface Waves With Higher Modes

Advantages of calculating shear-wave velocity from surface waves with higher modes Jianghai Xia,* Richard D. Miller, and Choon B. Park, Kansas Geological Survey Summary The Rayleigh-wave phase velocity of a layered earth model is a function of frequency and four groups of earth parameters: com- pressional (P)-wave velocity, shear (S)-wave velocity, density, and thickness of layers. For the fundamental mode of Rayleigh waves, analysis of the Jacobian matrix for high frequencies (5-40 Hz) provides a measure of dispersion curve sensitivity to earth model parameters. S-wave velocities are the dominant influence of the four earth model parameters. With the lack of sensitivity of the Rayleigh wave to P-wave velocities and densities, estimations of these parameters can be made for a layered earth model such that dispersive data vary predominantly with S-wave velocities (Xia et al., 1999a). This thesis is valid for higher modes of Rayleigh waves as well. Experimental analysis indicates that energy of higher modes tends to become more dominant as the source distance becomes larger (Park et al., 1999a). In some cases, higher mode data are necessary since shorter wavelength components of fundamental mode Rayleigh waves are obscured by these higher frequency data where higher modes of Rayleigh waves dominate. As well, our modeling results demonstrate at least two quite exciting higher mode properties. First, for fundamental and higher mode Rayleigh wave data with the same wavelength, higher modes can “see” deeper (longer than the wavelength) than fundamental modes (normally shorter than the wavelength). Second, high er mode data can increase the resolution of the inverted S-wave velocities. A much better S-wave velocity picture can be produced from inversion of surface wave data if higher-mode data are included. Real world examples show how resolution can be improved. Introduction Elastic properties of near-surface materials and their effects on seismic wave propagation are of fundamental interest in ground- water, engineering, and environmental studies. S-wave velocity is used to determine “stiffness,” one of the key earth properties in construction engineering. Shear-wave velocity as a function of depth can be derived from inverting the phase velocity of the surface (Rayleigh and/or Love) wave (Dorman and Ewing, 1962). Surface waves are guided and dispersive. Rayleigh (1885) waves are surface waves that travel along a “free” surface, such as the earth-air interface and are the result of interfering P and S v waves. Particle motion of Rayleigh waves moving from left to right is elliptical in a counter-clockwise (retrograde) direction. This motion is constrained to a vertical plane, consistent with the direction of wave propagation (p. 30, Babuska and Cara, 1991). Longer wavelengths penetrate deeper than shorter wavelengths for a given mode and in general exhibit greater phase velocities and are more sensitive to the elastic properties of deeper layers (p. 30, Babuska and Cara, 1991). Shorter wavelengths are sensitive to the physical properties of surficial layers. For this reason, surface waves possess a unique phase velocity for each unique wavelength, which results in dispersion characteristics . A series of Rayleigh waves of different frequencies can have the same wave velocity. These different frequency Rayleigh waves for a given phase velocity are known as modes and are characterized by their different number of horizontal nodal planes (planes of no particle displacement within the layer) (p. 60, Garland, 1979). In other words, more than one phase velocity can be associated with a given frequency of Rayleigh wave simply because these waves can travel at different velocities for a given frequency. The lowest velocity for any given frequency is called the fundamental-mode velocity (or the first mode). The next higher velocity above the fundamental-mode phase velocity is called the second-mode velocity , and so on . Ground roll is a particular type of Rayleigh wave that travels along or near the ground surface and is usually characterized by relatively low velocity, low frequency, and high amplitude (p. 143, Sheriff, 1991). Stokoe and Nazarian (1983) presented a surface-wave method, Spectral Analysis of Surface Waves (SASW), that analyzes the dispersion curve of ground roll to produce near-surface S-wave velocity profiles. A research group of the Kansas Geological Survey (KGS) investigated how to estimate the S-wave velocity from ground roll, focusing mainly on the fundamental mode of Rayleigh waves. The resulting technique consists of: 1) acquisition of wide band ground roll using a multi-channel recording system; 2) creation of efficient and accurate algorithms designed to extract Raylei gh- wave dispersion curves from ground roll using a basic, robust, and pseudo-automated processing sequence; and 3) development of stable and efficient inversion algorithms to obtain S-wave velocity profiles. The main product of this research, called Multi- channel Analysis of Surface Waves (MASW), has been published by Park et al. (1999b), Xia et al. (1998 and 1999a), and Miller et al., (1999). Based on experience, the fundamental-mode phase velocities when calculated with high accuracy (e.g., Xia et al., 1999b) can generally provide reliable Vs velocities (±15%). However, in cases where estimations of the fundamental-mode phase velocities are associated with high degree of error (e.g., if the fundamental-mode Rayleigh waves are contaminated by body waves and/or SEG 2000 Expanded Abstracts SEG 2000 Expanded Abstracts

Advantages of Calculating Shear-wave Velocity From Surface Waves With Higher Modes

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